A Dynamic Phase Transition Model for Spatial Agglomeration Processes*

Weidlich, Wolfgang; Haag, Günter

doi:10.1111/j.1467-9787.1987.tb01181.x

Cited by 57 publications

(27 citation statements)

References 8 publications

(1 reference statement)

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“…For example, the master equation has found many applications in thermodynamics [1], chemical kinetics [2], laser theory [3] and biology [4]. Moreover, Weidlich and Haag have successfully introduced it for the description of social processes [5,6] like opinion formation [7], migration [8], agglomeration [9] and settlement processes [10].…”

Section: Introductionmentioning

confidence: 99%

Boltzmann-like and Boltzmann-Fokker-Planck equations as a foundation of behavioral models

Helbing

1993

Physica A: Statistical Mechanics and its Applications

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It is shown, that the Boltzmann-like equations allow the formulation of a very general model for behavioral changes. This model takes into account spontaneous (or externally induced) behavioral changes and behavioral changes by pair interactions. As most important social pair interactions imitative and avoidance processes are distinguished. The resulting model turns out to include as special cases many theoretical concepts of the social sciences.A Kramers-Moyal expansion of the Boltzmann-like equations leads to the Boltzmann-Fokker-Planck equations, which allows the introduction of "social forces" and "social fields". A social field reflects the influence of the public opinion, social norms and trends on behaviorial changes. It is not only given by external factors (the environment) but also by the interactions of the individuals. Variations of the individual behavior are taken into account by diffusion coefficients.

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Section: Introductionmentioning

confidence: 99%

Boltzmann-like and Boltzmann-Fokker-Planck equations as a foundation of behavioral models

Helbing

1993

Physica A: Statistical Mechanics and its Applications

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“…Le concept de « structure dissipative » a été introduit par Prigogine de l'École de Bruxelles (voir Nicolis et Prigogine, 1977). Il est proche du concept de « synergie » introduit par Haken (voir Haken 1993et Weidlich et Haag, 1987. Dans ce nouveau cadre de référence se pose la question essentielle de la stabilité des états de tels systèmes dynamiques.…”

Section: Le Cas Des Villesunclassified

Le Grand Paris : Quels outils, quels enjeux ?

Palma¹

2015

Tables Rondes FIT

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in FORUM INTERNATIONAL DES TRANSPORTSLe Forum International des Transports, lié à l'OCDE, est une organisation intergouvernementale comprenant 52 pays membres. Le Forum mène une analyse politique stratégique dans le domaine des transports avec l'ambition d'aider à façonner l'agenda politique mondial des transports, et de veiller à ce qu'il contribue à la croissance économique, la protection de l'environnement, la cohésion sociale et la préservation de la vie humaine et du bien-être. Le Forum International des Transports organise un sommet ministériel annuel avec des décideurs du monde des affaires, des représentants clés de la société civile ainsi que des chercheurs éminents.Le Forum International des Transports a été créé par une Déclaration du Conseil des Ministres de la CEMT (Conférence Européenne des Ministres des Transports) lors de la session ministérielle de mai 2006. Il est établi sur la base juridique du Protocole de la CEMT signé à Bruxelles le 17 octobre 1953 ainsi que des instruments juridiques appropriés de l'OCDE. Son Secrétariat se trouve à Paris.

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“…Bifurcations, chaotic dynamics, phase transitions and other interesting behaviours are effectively observed in many of these models of socioeconomical systems [ibidem and e.g. Weidlich, 1990a and1990b;Weidlich and Haag, 1987;Popkov, Shvetsov and Weidlich, 1998]. …”

Section: State Of the Artmentioning

confidence: 99%

A Model for Urban Growth Processes with Continuum State Cellular Automata and Related Differential Equations

et al. 2004

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A new kind of cellular automaton (CA) for the study of the dynamics of urban systems is proposed. The state of a cell is not described using a finite set, but by means of continuum variables. A population sector is included, taking into account migration processes from and towards the external world. The transport network is considered through an integration index describing the capability of the network to interconnect the different parts of the city. The time evolution is given by Poisson distributed stochastic jumps affecting the dynamical variables, with intensities depending on the configuration of the system in a suitable set of neighbourhoods. The intensities of the Poisson processes are given in term of a set of potentials evaluated applying fuzzy logic to a practical method frequently used in Switzerland to evaluate the attractiveness of a terrain for different land uses and the related rents. The use of a continuum state space enables one to write a system of differential equations for the time evolution of the CA and thus to study the system from a dynamical systems theory perspective. This makes it possible, in particular, to look systematically for bifurcations and phase transitions in CA based models of urban systems.

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A Dynamic Phase Transition Model for Spatial Agglomeration Processes*

Cited by 57 publications

References 8 publications

Boltzmann-like and Boltzmann-Fokker-Planck equations as a foundation of behavioral models

Boltzmann-like and Boltzmann-Fokker-Planck equations as a foundation of behavioral models

Le Grand Paris : Quels outils, quels enjeux ?

A Model for Urban Growth Processes with Continuum State Cellular Automata and Related Differential Equations

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